Question

if A(1,2),B(4,3)AND C(6,6) ARE THE VERTICES OF PARALLELOGRAM ABCD ,THEN FIND THE CO ORDINATE OF THE FOURTH VERTICES.

Answer 1

Let D(a,b) be the 4th vertex.

Midpoint of AC = (1+6/2,2+6/2) = (7/2,4)       

Midpoint of BD = (a+4/2,b+3/2)


 a+4/2 = 7/2 , b+3/2 = 4

a + 4 = 7, b + 3 = 8

a = 3, b = 5


Hope this helps!

Answer 2

Answer:

The coordinates of the fourth vertex of the parallelogram are (3,5).

Step-by-step explanation:

The three coordinates of a parallelogram ABCD are A(1,2), B(4,3), and C(6,6).

We need to Calculate the coordinates of the fourth vertex.

Let the fourth vertex's coordinates be ( a,b )

We join the diagonals of the parallelogram,

The diagonals are AC and BD.

The midpoint of AC is $(\frac{1+6}{2}, \frac{2+6}{2} ) = (\frac{7}{2} ,4)$

Now, we calculate the midpoint of the other diagonal BD,

So, the midpoint of diagonal BD is $(\frac{a+4}{2},\frac{3+b}{2} )$

Now, the midpoints of both diagonals have to be the same.

So, $(\frac{7}{2} ,4) =(\frac{a+4}{2},\frac{3+b}{2} )$

Now,

$\frac{a+4}{2} = \frac{7}{2}\\a + 4 = 7\\a = 7 - 4 = 3$

For the y coordinate,

$\frac{3+b}{2} =4\\3 +b = 8\\b = 8 -3 = 5$

Therefore, the coordinates of the fourth vertex are (3,5).

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